Isabelle Bloch is Professor at the Ecole Nationale Supérieure desTélécommunications, Paris, France.

• Preface 11Isabelle BLOCHChapter 1. Definitions 13Isabelle BLOCH and Henri MAÎTRE1.1. Introduction 131.2. Choosing a definition 131.3. General characteristics of the data 161.4. Numerical/symbolic 191.4.1. Data and information 191.4.2. Processes 191.4.3. Representations 201.5. Fusion systems 201.6. Fusion in signal and image processing and fusion in other fields 221.7. Bibliography 23Chapter 2. Fusion in Signal Processing 25Jean-Pierre LE CADRE, Vincent NIMIER and Roger REYNAUD2.1. Introduction 252.2. Objectives of fusion in signal processing 272.2.1. Estimation and calculation of a law a posteriori 282.2.2. Discriminating between several hypotheses and identifying 312.2.3. Controlling and supervising a data fusion chain 342.3. Problems and specificities of fusion in signal processing 372.3.1. Dynamic control 372.3.2. Quality of the information 422.3.3. Representativeness and accuracy of learning and a priori information 432.4. Bibliography 43Chapter 3. Fusion in Image Processing 47Isabelle BLOCH and Henri MAÎTRE3.1. Objectives of fusion in image processing 473.2. Fusion situations 503.3. Data characteristics in image fusion 513.4. Constraints 543.5. Numerical and symbolic aspects in image fusion 553.6. Bibliography 56Chapter 4. Fusion in Robotics 57Michèle ROMBAUT4.1. The necessity for fusion in robotics 574.2. Specific features of fusion in robotics 584.2.1.Constraints on the perception system 584.2.2. Proprioceptive and exteroceptive sensors 584.2.3. Interaction with the operator and symbolic interpretation 594.2.4. Time constraints 594.3. Characteristics of the data in robotics 614.3.1. Calibrating and changing the frame of reference 614.3.2. Types and levels of representation of the environment 624.4. Data fusion mechanisms 634.5. Bibliography 64Chapter 5. Information and Knowledge Representation in Fusion Problems 65Isabelle BLOCH and Henri MAÎTRE5.1. Introduction 655.2. Processing information in fusion 655.3. Numerical representations of imperfect knowledge 675.4. Symbolic representation of imperfect knowledge 685.5. Knowledge-based systems 695.6. Reasoning modes and inference 735.7. Bibliography 74Chapter 6. Probabilistic and Statistical Methods 77Isabelle BLOCH, Jean-Pierre LE CADRE and Henri MAÎTRE6.1. Introduction and general concepts 776.2. Information measurements 776.3. Modeling and estimation 796.4. Combination in a Bayesian framework 806.5. Combination as an estimation problem 806.6. Decision 816.7. Other methods in detection 816.8. An example of Bayesian fusion in satellite imagery 826.9. Probabilistic fusion methods applied to target motion analysis 846.9.1. General presentation 846.9.2. Multi-platform target motion analysis 956.9.3. Target motion analysis by fusion of active and passive measurements 966.9.4. Detection of a moving target in a network of sensors 986.10. Discussion 1016.11. Bibliography 104Chapter 7. Belief Function Theory 107Isabelle BLOCH7.1. General concept and philosophy of the theory 1077.2. Modeling 1087.3. Estimation of mass functions 1117.3.1. Modification of probabilistic models 1127.3.2. Modification of distance models 1147.3.3. A priori information on composite focal elements (disjunctions) 1147.3.4. Learning composite focal elements 1157.3.5. Introducing disjunctions by mathematical morphology 1157.4. Conjunctive combination 1167.4.1. Dempster’s rule 1167.4.2. Conflict and normalization 1167.4.3. Properties 1187.4.4. Discounting 1207.4.5. Conditioning 1207.4.6. Separable mass functions 1217.4.7. Complexity 1227.5. Other combination modes 1227.6. Decision 1227.7. Application example in medical imaging 1247.8. Bibliography 131Chapter 8. Fuzzy Sets and Possibility Theory 135Isabelle BLOCH8.1. Introduction and general concepts 1358.2. Definitions of the fundamental concepts of fuzzy sets 1368.2.1. Fuzzy sets 1368.2.2. Set operations: Zadeh’s original definitions 1378.2.3. α-cuts 1398.2.4. Cardinality 1398.2.5. Fuzzy number 1408.3. Fuzzy measures 142 8.3.1. Fuzzy measure of a crisp set 1428.3.2. Examples of fuzzy measures 1428.3.3. Fuzzy integrals 1438.3.4. Fuzzy set measures 1458.3.5. Measures of fuzziness 1458.4. Elements of possibility theory 1478.4.1. Necessity and possibility 1478.4.2. Possibility distribution 1488.4.3. Semantics 1508.4.4. Similarities with the probabilistic, statistical and belief interpretations 1508.5. Combination operators 1518.5.1. Fuzzy complementation 1528.5.2. Triangular norms and conorms 1538.5.3. Mean operators 1618.5.4. Symmetric sums 1658.5.5. Adaptive operators 1678.6. Linguistic variables 1708.6.1. Definition 1718.6.2. An example of a linguistic variable 1718.6.3. Modifiers 1728.7. Fuzzy and possibilistic logic 1728.7.1. Fuzzy logic 1738.7.2. Possibilistic logic 1778.8. Fuzzy modeling in fusion 1798.9. Defining membership functions or possibility distributions 1808.10. Combining and choosing the operators 1828.11. Decision 1878.12. Application examples 1888.12.1. Example in satellite imagery 1888.12.2. Example in medical imaging 1928.13. Bibliography 194Chapter 9. Spatial Information in Fusion Methods 199Isabelle BLOCH9.1. Modeling 1999.2. The decision level 2009.3. The combination level 2019.4. Application examples 2019.4.1. The combination level: multi-source Markovian classification 2019.4.2. The modeling and decision level: fusion of structure detectors using belief function theory 2029.4.3. The modeling level: fuzzy fusion of spatial relations 2059.5. Bibliography 211Chapter 10. Multi-Agent Methods: An Example of an Architecture and its Application for the Detection, Recognition and Identification of Targets 213Fabienne EALET, Bertrand COLLIN and Catherine GARBAY10.1.The DRI function 21410.1.1. The application context 21510.1.2. Design constraints and concepts 21610.1.3. State of the art 21610.2. Proposed method: towards a vision system 21710.2.1. Representation space and situated agents 21810.2.2. Focusing and adapting 21910.2.3. Distribution and co-operation 22010.2.4. Decision and uncertainty management 22110.2.5. Incrementality and learning 22110.3. The multi-agent system: platform and architecture 22210.3.1. The developed multi-agent architecture 22210.3.2. Presentation of the platformused 22210.4. The control scheme 22410.4.1. The intra-image control cycle 22410.4.2. Inter-image control cycle 22610.5. The information handled by the agents 22710.5.1. The knowledge base 22710.5.2. The world model 22910.6. The results 23110.6.1. Direct analysis 23210.6.2. Indirect analysis: two focusing strategies 23510.6.3. Indirect analysis: spatial and temporal exploration 23710.6.4. Conclusion 24010.7. Bibliography 241Chapter 11. Fusion of Non-Simultaneous Elements of Information: Temporal Fusion 245Michèle ROMBAUT11.1. Time variable observations 24511.2. Temporal constraints 24611.3. Fusion 24711.3.1. Fusion of distinct sources 24711.3.2. Fusion of single source data 24811.3.3. Temporal registration 24911.4. Dating measurements 24911.5. Evolutionary models 25011.6. Single sensor prediction-combination 25211.7. Multi-sensor prediction-combination 25311.8. Conclusion 25711.9. Bibliography 257Chapter 12. Conclusion 259Isabelle BLOCH12.1. A few achievements 25912.2. A few prospects 26012.3. Bibliography 261Appendices 263A. Probabilities: A Historical Perspective 263A.1. Probabilities through history 264A.1.1. Before 1660 264A.1.2. Towards the Bayesian mathematical formulation 266A.1.3. The predominance of the frequentist approach: the “objectivists” 268A.1.4. The 20th century: a return to subjectivism 269A.2. Objectivist and subjectivist probability classes 271A.3. Fundamental postulates for an inductive logic 272A.3.1. Fundamental postulates 273A.3.2. First functional equation 274A.3.3. Second functional equation 275A.3.4. Probabilities inferred from functional equations 276A.3.5. Measure of uncertainty and information theory 276A.3.6. De Finetti and betting theory 277A.4.Bibliography 280B. Axiomatic Inference of the Dempster-Shafer Combination Rule 283B.1. Smets’s axioms 284B.2. Inference of the combination rule 286B.3.RelationwithCox’s postulates 287B.4.Bibliography 289List of Authors 291Index 293

Isabelle Bloch is Professor at the Ecole Nationale Supérieure desTélécommunications, Paris, France.

• Preface 11Isabelle BLOCHChapter 1. Definitions 13Isabelle BLOCH and Henri MAÎTRE1.1. Introduction 131.2. Choosing a definition 131.3. General characteristics of the data 161.4. Numerical/symbolic 191.4.1. Data and information 191.4.2. Processes 191.4.3. Representations 201.5. Fusion systems 201.6. Fusion in signal and image processing and fusion in other fields 221.7. Bibliography 23Chapter 2. Fusion in Signal Processing 25Jean-Pierre LE CADRE, Vincent NIMIER and Roger REYNAUD2.1. Introduction 252.2. Objectives of fusion in signal processing 272.2.1. Estimation and calculation of a law a posteriori 282.2.2. Discriminating between several hypotheses and identifying 312.2.3. Controlling and supervising a data fusion chain 342.3. Problems and specificities of fusion in signal processing 372.3.1. Dynamic control 372.3.2. Quality of the information 422.3.3. Representativeness and accuracy of learning and a priori information 432.4. Bibliography 43Chapter 3. Fusion in Image Processing 47Isabelle BLOCH and Henri MAÎTRE3.1. Objectives of fusion in image processing 473.2. Fusion situations 503.3. Data characteristics in image fusion 513.4. Constraints 543.5. Numerical and symbolic aspects in image fusion 553.6. Bibliography 56Chapter 4. Fusion in Robotics 57Michèle ROMBAUT4.1. The necessity for fusion in robotics 574.2. Specific features of fusion in robotics 584.2.1.Constraints on the perception system 584.2.2. Proprioceptive and exteroceptive sensors 584.2.3. Interaction with the operator and symbolic interpretation 594.2.4. Time constraints 594.3. Characteristics of the data in robotics 614.3.1. Calibrating and changing the frame of reference 614.3.2. Types and levels of representation of the environment 624.4. Data fusion mechanisms 634.5. Bibliography 64Chapter 5. Information and Knowledge Representation in Fusion Problems 65Isabelle BLOCH and Henri MAÎTRE5.1. Introduction 655.2. Processing information in fusion 655.3. Numerical representations of imperfect knowledge 675.4. Symbolic representation of imperfect knowledge 685.5. Knowledge-based systems 695.6. Reasoning modes and inference 735.7. Bibliography 74Chapter 6. Probabilistic and Statistical Methods 77Isabelle BLOCH, Jean-Pierre LE CADRE and Henri MAÎTRE6.1. Introduction and general concepts 776.2. Information measurements 776.3. Modeling and estimation 796.4. Combination in a Bayesian framework 806.5. Combination as an estimation problem 806.6. Decision 816.7. Other methods in detection 816.8. An example of Bayesian fusion in satellite imagery 826.9. Probabilistic fusion methods applied to target motion analysis 846.9.1. General presentation 846.9.2. Multi-platform target motion analysis 956.9.3. Target motion analysis by fusion of active and passive measurements 966.9.4. Detection of a moving target in a network of sensors 986.10. Discussion 1016.11. Bibliography 104Chapter 7. Belief Function Theory 107Isabelle BLOCH7.1. General concept and philosophy of the theory 1077.2. Modeling 1087.3. Estimation of mass functions 1117.3.1. Modification of probabilistic models 1127.3.2. Modification of distance models 1147.3.3. A priori information on composite focal elements (disjunctions) 1147.3.4. Learning composite focal elements 1157.3.5. Introducing disjunctions by mathematical morphology 1157.4. Conjunctive combination 1167.4.1. Dempster’s rule 1167.4.2. Conflict and normalization 1167.4.3. Properties 1187.4.4. Discounting 1207.4.5. Conditioning 1207.4.6. Separable mass functions 1217.4.7. Complexity 1227.5. Other combination modes 1227.6. Decision 1227.7. Application example in medical imaging 1247.8. Bibliography 131Chapter 8. Fuzzy Sets and Possibility Theory 135Isabelle BLOCH8.1. Introduction and general concepts 1358.2. Definitions of the fundamental concepts of fuzzy sets 1368.2.1. Fuzzy sets 1368.2.2. Set operations: Zadeh’s original definitions 1378.2.3. α-cuts 1398.2.4. Cardinality 1398.2.5. Fuzzy number 1408.3. Fuzzy measures 142 8.3.1. Fuzzy measure of a crisp set 1428.3.2. Examples of fuzzy measures 1428.3.3. Fuzzy integrals 1438.3.4. Fuzzy set measures 1458.3.5. Measures of fuzziness 1458.4. Elements of possibility theory 1478.4.1. Necessity and possibility 1478.4.2. Possibility distribution 1488.4.3. Semantics 1508.4.4. Similarities with the probabilistic, statistical and belief interpretations 1508.5. Combination operators 1518.5.1. Fuzzy complementation 1528.5.2. Triangular norms and conorms 1538.5.3. Mean operators 1618.5.4. Symmetric sums 1658.5.5. Adaptive operators 1678.6. Linguistic variables 1708.6.1. Definition 1718.6.2. An example of a linguistic variable 1718.6.3. Modifiers 1728.7. Fuzzy and possibilistic logic 1728.7.1. Fuzzy logic 1738.7.2. Possibilistic logic 1778.8. Fuzzy modeling in fusion 1798.9. Defining membership functions or possibility distributions 1808.10. Combining and choosing the operators 1828.11. Decision 1878.12. Application examples 1888.12.1. Example in satellite imagery 1888.12.2. Example in medical imaging 1928.13. Bibliography 194Chapter 9. Spatial Information in Fusion Methods 199Isabelle BLOCH9.1. Modeling 1999.2. The decision level 2009.3. The combination level 2019.4. Application examples 2019.4.1. The combination level: multi-source Markovian classification 2019.4.2. The modeling and decision level: fusion of structure detectors using belief function theory 2029.4.3. The modeling level: fuzzy fusion of spatial relations 2059.5. Bibliography 211Chapter 10. Multi-Agent Methods: An Example of an Architecture and its Application for the Detection, Recognition and Identification of Targets 213Fabienne EALET, Bertrand COLLIN and Catherine GARBAY10.1.The DRI function 21410.1.1. The application context 21510.1.2. Design constraints and concepts 21610.1.3. State of the art 21610.2. Proposed method: towards a vision system 21710.2.1. Representation space and situated agents 21810.2.2. Focusing and adapting 21910.2.3. Distribution and co-operation 22010.2.4. Decision and uncertainty management 22110.2.5. Incrementality and learning 22110.3. The multi-agent system: platform and architecture 22210.3.1. The developed multi-agent architecture 22210.3.2. Presentation of the platformused 22210.4. The control scheme 22410.4.1. The intra-image control cycle 22410.4.2. Inter-image control cycle 22610.5. The information handled by the agents 22710.5.1. The knowledge base 22710.5.2. The world model 22910.6. The results 23110.6.1. Direct analysis 23210.6.2. Indirect analysis: two focusing strategies 23510.6.3. Indirect analysis: spatial and temporal exploration 23710.6.4. Conclusion 24010.7. Bibliography 241Chapter 11. Fusion of Non-Simultaneous Elements of Information: Temporal Fusion 245Michèle ROMBAUT11.1. Time variable observations 24511.2. Temporal constraints 24611.3. Fusion 24711.3.1. Fusion of distinct sources 24711.3.2. Fusion of single source data 24811.3.3. Temporal registration 24911.4. Dating measurements 24911.5. Evolutionary models 25011.6. Single sensor prediction-combination 25211.7. Multi-sensor prediction-combination 25311.8. Conclusion 25711.9. Bibliography 257Chapter 12. Conclusion 259Isabelle BLOCH12.1. A few achievements 25912.2. A few prospects 26012.3. Bibliography 261Appendices 263A. Probabilities: A Historical Perspective 263A.1. Probabilities through history 264A.1.1. Before 1660 264A.1.2. Towards the Bayesian mathematical formulation 266A.1.3. The predominance of the frequentist approach: the “objectivists” 268A.1.4. The 20th century: a return to subjectivism 269A.2. Objectivist and subjectivist probability classes 271A.3. Fundamental postulates for an inductive logic 272A.3.1. Fundamental postulates 273A.3.2. First functional equation 274A.3.3. Second functional equation 275A.3.4. Probabilities inferred from functional equations 276A.3.5. Measure of uncertainty and information theory 276A.3.6. De Finetti and betting theory 277A.4.Bibliography 280B. Axiomatic Inference of the Dempster-Shafer Combination Rule 283B.1. Smets’s axioms 284B.2. Inference of the combination rule 286B.3.RelationwithCox’s postulates 287B.4.Bibliography 289List of Authors 291Index 293

Isabelle Bloch is Professor at the Ecole Nationale Supérieure desTélécommunications, Paris, France.

• Preface 11Isabelle BLOCHChapter 1. Definitions 13Isabelle BLOCH and Henri MAÎTRE1.1. Introduction 131.2. Choosing a definition 131.3. General characteristics of the data 161.4. Numerical/symbolic 191.4.1. Data and information 191.4.2. Processes 191.4.3. Representations 201.5. Fusion systems 201.6. Fusion in signal and image processing and fusion in other fields 221.7. Bibliography 23Chapter 2. Fusion in Signal Processing 25Jean-Pierre LE CADRE, Vincent NIMIER and Roger REYNAUD2.1. Introduction 252.2. Objectives of fusion in signal processing 272.2.1. Estimation and calculation of a law a posteriori 282.2.2. Discriminating between several hypotheses and identifying 312.2.3. Controlling and supervising a data fusion chain 342.3. Problems and specificities of fusion in signal processing 372.3.1. Dynamic control 372.3.2. Quality of the information 422.3.3. Representativeness and accuracy of learning and a priori information 432.4. Bibliography 43Chapter 3. Fusion in Image Processing 47Isabelle BLOCH and Henri MAÎTRE3.1. Objectives of fusion in image processing 473.2. Fusion situations 503.3. Data characteristics in image fusion 513.4. Constraints 543.5. Numerical and symbolic aspects in image fusion 553.6. Bibliography 56Chapter 4. Fusion in Robotics 57Michèle ROMBAUT4.1. The necessity for fusion in robotics 574.2. Specific features of fusion in robotics 584.2.1.Constraints on the perception system 584.2.2. Proprioceptive and exteroceptive sensors 584.2.3. Interaction with the operator and symbolic interpretation 594.2.4. Time constraints 594.3. Characteristics of the data in robotics 614.3.1. Calibrating and changing the frame of reference 614.3.2. Types and levels of representation of the environment 624.4. Data fusion mechanisms 634.5. Bibliography 64Chapter 5. Information and Knowledge Representation in Fusion Problems 65Isabelle BLOCH and Henri MAÎTRE5.1. Introduction 655.2. Processing information in fusion 655.3. Numerical representations of imperfect knowledge 675.4. Symbolic representation of imperfect knowledge 685.5. Knowledge-based systems 695.6. Reasoning modes and inference 735.7. Bibliography 74Chapter 6. Probabilistic and Statistical Methods 77Isabelle BLOCH, Jean-Pierre LE CADRE and Henri MAÎTRE6.1. Introduction and general concepts 776.2. Information measurements 776.3. Modeling and estimation 796.4. Combination in a Bayesian framework 806.5. Combination as an estimation problem 806.6. Decision 816.7. Other methods in detection 816.8. An example of Bayesian fusion in satellite imagery 826.9. Probabilistic fusion methods applied to target motion analysis 846.9.1. General presentation 846.9.2. Multi-platform target motion analysis 956.9.3. Target motion analysis by fusion of active and passive measurements 966.9.4. Detection of a moving target in a network of sensors 986.10. Discussion 1016.11. Bibliography 104Chapter 7. Belief Function Theory 107Isabelle BLOCH7.1. General concept and philosophy of the theory 1077.2. Modeling 1087.3. Estimation of mass functions 1117.3.1. Modification of probabilistic models 1127.3.2. Modification of distance models 1147.3.3. A priori information on composite focal elements (disjunctions) 1147.3.4. Learning composite focal elements 1157.3.5. Introducing disjunctions by mathematical morphology 1157.4. Conjunctive combination 1167.4.1. Dempster’s rule 1167.4.2. Conflict and normalization 1167.4.3. Properties 1187.4.4. Discounting 1207.4.5. Conditioning 1207.4.6. Separable mass functions 1217.4.7. Complexity 1227.5. Other combination modes 1227.6. Decision 1227.7. Application example in medical imaging 1247.8. Bibliography 131Chapter 8. Fuzzy Sets and Possibility Theory 135Isabelle BLOCH8.1. Introduction and general concepts 1358.2. Definitions of the fundamental concepts of fuzzy sets 1368.2.1. Fuzzy sets 1368.2.2. Set operations: Zadeh’s original definitions 1378.2.3. α-cuts 1398.2.4. Cardinality 1398.2.5. Fuzzy number 1408.3. Fuzzy measures 142 8.3.1. Fuzzy measure of a crisp set 1428.3.2. Examples of fuzzy measures 1428.3.3. Fuzzy integrals 1438.3.4. Fuzzy set measures 1458.3.5. Measures of fuzziness 1458.4. Elements of possibility theory 1478.4.1. Necessity and possibility 1478.4.2. Possibility distribution 1488.4.3. Semantics 1508.4.4. Similarities with the probabilistic, statistical and belief interpretations 1508.5. Combination operators 1518.5.1. Fuzzy complementation 1528.5.2. Triangular norms and conorms 1538.5.3. Mean operators 1618.5.4. Symmetric sums 1658.5.5. Adaptive operators 1678.6. Linguistic variables 1708.6.1. Definition 1718.6.2. An example of a linguistic variable 1718.6.3. Modifiers 1728.7. Fuzzy and possibilistic logic 1728.7.1. Fuzzy logic 1738.7.2. Possibilistic logic 1778.8. Fuzzy modeling in fusion 1798.9. Defining membership functions or possibility distributions 1808.10. Combining and choosing the operators 1828.11. Decision 1878.12. Application examples 1888.12.1. Example in satellite imagery 1888.12.2. Example in medical imaging 1928.13. Bibliography 194Chapter 9. Spatial Information in Fusion Methods 199Isabelle BLOCH9.1. Modeling 1999.2. The decision level 2009.3. The combination level 2019.4. Application examples 2019.4.1. The combination level: multi-source Markovian classification 2019.4.2. The modeling and decision level: fusion of structure detectors using belief function theory 2029.4.3. The modeling level: fuzzy fusion of spatial relations 2059.5. Bibliography 211Chapter 10. Multi-Agent Methods: An Example of an Architecture and its Application for the Detection, Recognition and Identification of Targets 213Fabienne EALET, Bertrand COLLIN and Catherine GARBAY10.1.The DRI function 21410.1.1. The application context 21510.1.2. Design constraints and concepts 21610.1.3. State of the art 21610.2. Proposed method: towards a vision system 21710.2.1. Representation space and situated agents 21810.2.2. Focusing and adapting 21910.2.3. Distribution and co-operation 22010.2.4. Decision and uncertainty management 22110.2.5. Incrementality and learning 22110.3. The multi-agent system: platform and architecture 22210.3.1. The developed multi-agent architecture 22210.3.2. Presentation of the platformused 22210.4. The control scheme 22410.4.1. The intra-image control cycle 22410.4.2. Inter-image control cycle 22610.5. The information handled by the agents 22710.5.1. The knowledge base 22710.5.2. The world model 22910.6. The results 23110.6.1. Direct analysis 23210.6.2. Indirect analysis: two focusing strategies 23510.6.3. Indirect analysis: spatial and temporal exploration 23710.6.4. Conclusion 24010.7. Bibliography 241Chapter 11. Fusion of Non-Simultaneous Elements of Information: Temporal Fusion 245Michèle ROMBAUT11.1. Time variable observations 24511.2. Temporal constraints 24611.3. Fusion 24711.3.1. Fusion of distinct sources 24711.3.2. Fusion of single source data 24811.3.3. Temporal registration 24911.4. Dating measurements 24911.5. Evolutionary models 25011.6. Single sensor prediction-combination 25211.7. Multi-sensor prediction-combination 25311.8. Conclusion 25711.9. Bibliography 257Chapter 12. Conclusion 259Isabelle BLOCH12.1. A few achievements 25912.2. A few prospects 26012.3. Bibliography 261Appendices 263A. Probabilities: A Historical Perspective 263A.1. Probabilities through history 264A.1.1. Before 1660 264A.1.2. Towards the Bayesian mathematical formulation 266A.1.3. The predominance of the frequentist approach: the “objectivists” 268A.1.4. The 20th century: a return to subjectivism 269A.2. Objectivist and subjectivist probability classes 271A.3. Fundamental postulates for an inductive logic 272A.3.1. Fundamental postulates 273A.3.2. First functional equation 274A.3.3. Second functional equation 275A.3.4. Probabilities inferred from functional equations 276A.3.5. Measure of uncertainty and information theory 276A.3.6. De Finetti and betting theory 277A.4.Bibliography 280B. Axiomatic Inference of the Dempster-Shafer Combination Rule 283B.1. Smets’s axioms 284B.2. Inference of the combination rule 286B.3.RelationwithCox’s postulates 287B.4.Bibliography 289List of Authors 291Index 293